Samurai spirit
The samurai was a special class of warriors that were educated with high discipline, loyalty, courage and decision to die before to brake their code of honor.  Karatekas take most of the Bushido as his own ethic code. The samurai of bushi were loyal to their masters and karatekas are free of this part.  The karatekas' has Budo as their own code of ethics but they still train karate using part of the Bushido code.
Bushido means the way of the warrior
Physical endurance
The same as the samurai did, karate practioners know that pain is not a limitation to our hard work. Pain is part of the hard training to endure the spirit and the body.  It does not means that we enjoy the pain but we take it as sign and a mesure of the physical and mental work that we do looking to perfect our techniques.
Budo is the code of karate practitioners.  By practicing karate we look to become a humble person destroying our ego.  Budo teach us the way to avoid the combat, or stop the fight.  In karate we never attack first.
Budo means the way to stop the conflict or fight